{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"amc","formal_name":"AMC (AIMO validation set)","introduction":"83 AMC 12 problems assembled by Project Numina as a validation set for the AIMO competition. They sit a step below AIME in difficulty, which makes them a useful lower rung on the same scale.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"a30d9527-13b3-50b1-a4cf-6c7e36b668f3","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f6","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_6","short_description":"Consider the following $100$ sets of $10$ elements each:","config":"default","split":"train","body":"{\"problem\":\"Consider the following $100$ sets of $10$ elements each:\\n\\\\begin{align*} &\\\\{1,2,3,\\\\ldots,10\\\\}, \\\\\\\\ &\\\\{11,12,13,\\\\ldots,20\\\\},\\\\\\\\ &\\\\{21,22,23,\\\\ldots,30\\\\},\\\\\\\\ &\\\\vdots\\\\\\\\ &\\\\{991,992,993,\\\\ldots,1000\\\\}. \\\\end{align*}\\nHow many of these sets contain exactly two multiples of $7$?\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}